Problem: Factor completely. $7x^2+28x-35=$
Answer: First, let's factor out the greatest common factor. If the leading coefficient is negative, we'll also factor out $-1$. The result will be something like this, where the blanks are coefficients: $_{\llcorner\!\lrcorner}\!(_{\llcorner\!\lrcorner}\! x^2+\, _{\llcorner\!\lrcorner}\! x+\, _{\llcorner\!\lrcorner}\!)$ Then, we can try to factor the sum like this: $_{\llcorner\!\lrcorner}\!(_{\llcorner\!\lrcorner}\! x+\, _{\llcorner\!\lrcorner}\!) (_{\llcorner\!\lrcorner}\! x+\, _{\llcorner\!\lrcorner}\!)$ Factor out a the greatest common factor The greatest common factor is $7$. $\begin{aligned} &\phantom{=}7x^2+28x-35 \\\\ &=7(x^2+4x-5) \end{aligned}$ [How did we find the greatest common factor?] Factor $x^2+4x-5$ $\begin{aligned} &\phantom{=}7x^2+28x-35 \\\\ &=7(x^2+4x-5) \\\\ &=7(x-1)(x+5) \end{aligned}$ [I want to see this step in more detail.] Answer $\begin{aligned} &\phantom{=}7x^2+28x-35 \\\\ &=7(x-1)(x+5) \end{aligned}$